A novel network-based continuous-time representation for process scheduling: Part II. General framework

In the first part of this series of papers we presented a new network-based continuous-time representation for the short-term scheduling of batch processes, which overcomes numerous shortcomings of existing approaches. In this second part, we discuss how this representation can be extended to address aspects such as: (i) preventive maintenance activities on unary resources (e.g., processing and storage units) that were planned ahead of time; (ii) resource-constrained changeover activities on processing and shared storage units; (iii) non-instantaneous resource-constrained material transfer activities; (iv) intermediate deliveries of raw materials and shipments of finished products at predefined times; and (v) scenarios where part of the schedule is fixed because it has been programmed in the previous scheduling horizon. The proposed integrated framework can be used to address a wide variety of process scheduling problems, many of which are intractable with existing tools.     

最佳间歇水循环网络的合成和时序安排

This work develops an optimization-based methodology for the design and scheduling of batch water recycle networks. This task requires the identification of network configuration, fresh-water usage, recycle assignments from sources to sinks, wastewater discharge, and a scheduling scheme. A new source-tank-sink representation is developed to allow for storage and dispatch tanks. The problem is solved in stages by first eliminating scheduling constraints and determining minimum usage of fresh water and wastewater discharge. An iterative procedure is formulated to minimize the total annual cost of the system by trading off capital versus operating costs. The work overcomes limitations in previous literature work including restricted recycle within the same cycle, lumped balances that may not lead to feasible solutions, and unrealistic objective functions. A case study is solved to illustrate the usefulness of the devised procedure.     

OPTIMAL DESIGN OF MULTIPLE BATCH UNITS WITH FEEDSTOCK/PRODUCT STORAGES

This article derives an analytical solution for determining the optimal size of the multiple batch unit plant with storage units. The total cost to be minimized consists of the setup cost of the batch processing units, the inventory holding cost of feedstock/product storage and the capital cost of the batch and storage units. A novel approach, which is called the PSW(Periodic Square Wave) model, is applied to represent the material flows among the batch and storage units. The PSW model presumes that the material flow between unit and storage is a periodic square shaped wave. The resulting optimal batch size has similar characteristics to the classical economic lot sizing model such as EOQ or EPQ model in the sense that the batch size is determined as the balance between setup and inventory holding cost. However, the influence of inventory holding cost of the PSW model is different from that of EOQ/EPQ model. The EOQ/ EPQ model includes only the product inventory holding cost while the PSW model includes all inventory holding costs around the batch unit.

The PSW model is suitable for analyzing interlinked batch-storage system and is more accurate rather than EOQ/EPQ model. The optimal lot size of the PSW model is much smaller than that of EOQ/EPQ model as shown at an example. This is quite a remarkable result considering that the EOQ/EPQ model has been widely used over the last half century.     

并联连续再生/再循环的多杂质间歇用水系统优化方法

为了有效地减少多杂质间歇用水系统的新鲜水消耗量和再生处理量,针对多杂质间歇过程用水网络提出连续操作并联再生处理单元水网络结构模型及其优化设计方法。通过在用水网络中设置中间储罐和再生单元以实现对不同水质废水并联分质处理,建立了减少用水系统的新鲜水用量和再生水量以及废水排放量的数学规划模型,采用GAMS软件对一个实例进行求解。计算和分析表明：提出的水网络结构与优化设计方法可有效地解决按水质对废水进行并联处理的间歇用水系统,使系统的新鲜水用量和再生水流率同时达到最小。     

Miniplants — Ein Beitrag zur inhärenten Sicherheit?

The scale minimisation of a chemical plant can increase its safety almost to the inherent safety level because the amounts of hazardous substances are greatly reduced. Because of the small amounts of hazardous substances usually present, miniplants, which have proved themselves in research and development, do not pose a serious danger to the environment. With regard to inherent safety, two concepts are presented which could help to avoid problems encountered in storage and transportation of hazardous substances and to lessen the hazardous potential of a chemical plant.     

MILP scheduling model for multipurpose batch processes considering various intermediate storage policies

MILP (Mixed Integer Linear Programming) scheduling models for non-sequential multipurpose batch processes are presented. Operation sequences of products have to be made in each unit differently by considering production route of each product under a given intermediate storage policy to reduce idle time of units and to raise the efficiency of the process. We represent the starting and finishing time of a task in each unit with two coordinates for a given storage policy. One is based on products, and the other is based on operation sequences. Then, using binary variables and logical constraints, we match the variables used in the two coordinates into one. We suggest MILP models considering sequence dependent setup times to guarantee the optimality of the solutions. Two examples are presented to show the effectiveness of the suggested models.     

Synthesis and sizing of batch/semicontinuous processes: single product plants

An approach is reported for the preliminary design of single product batch/semicontinuous plants. The methodology consists of two components: a new approximate sizing procedure, which determines the number of units in parallel at each stage as well as the sizes of the batch and semicontinuous units and a set of synthesis rules, which serve to select structural features such as consecutive tasks that should be merged or split and tasks that should be separated by intermediate storage. The sizing procedure can accommodate both new plant design as well as some simple forms of retrofitting applications. The effectiveness of the approach is demonstrated with comparisons to designs obtained using nonlinear programming formulations solved by using a generalized reduced-gradient algorithm.     

A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.     

OPTIMAL DESIGN OF MULTISITE BATCH-STORAGE NETWORK UNDER SCENARIO-BASED DEMAND UNCERTAINTY

An effective methodology is reported for the optimal design of multisite batch production/transportation and storage networks under uncertain demand forecasting. We assume that any given storage unit can store one material type that can be purchased from suppliers, internally produced, internally consumed, transported to or from other plant sites, and/or sold to customers. We further assume that a storage unit is connected to all processing and transportation stages that consume/produce or move the material to which that storage unit is dedicated. Each processing stage transforms a set of feedstock materials or intermediates into a set of products with constant conversion factors. A batch transportation process can transfer one material or multiple materials at once between plant sites. The objective for optimization is to minimize the probability averaged total cost, which consists of the raw material procurement cost, the cost of setting up processes, inventory holding costs of the storage units, and the capital costs of processes and storage units. A novel production and inventory analysis formulation, the PSW (periodic square wave) model, provides useful expressions for the upper/lower bounds and average level of the storage inventory. The expressions for the Kuhn-Tucker conditions of the optimization problem can be reduced to two sub-problems. The first yields analytical solutions for determining lot sizes, and the second is a separable concave minimization network flow sub-problem whose solution yields the average material flow rates through the networks for the given demand forecast scenario. The result of this study will contribute to the optimal design and operation of large-scale supply chain systems.     

考虑间接换热额外换热温差的间歇过程储热集成

间歇过程流股间换热有直接换热和间接换热两种方式,通过储热介质进行间接换热会产生额外的换热温差。现有的夹点分析方法考虑间接换热额外换热温差后,难以得到经济且可行的储热集成方案。本文在夹点分析的基础上,提出了一种考虑间接换热额外换热温差的间歇过程储热集成方法。该方法首先使用不同的直接换热和间接换热温差进行热级联分析,确定储热集成后的最小冷、热公用工程用量,识别储热位置和储热量,并依据热级联分析结果,建立时间段温焓图确定储热介质温度,得到储热方案。然后,将储热流股转化为放热时间段的冷流股和需热时间段的热流股,进行换热网络综合与优化,得到符合实际应用的储热集成方案。最后,通过经典实例证明了所提方法的可行性和有效性。     

Design of mixed energy‐integrated batch process networks by Pseudo‐direct approach

In this article, a novel framework for the design of mixed (combined direct and indirect) integration for batch process systems is presented. The framework is based on the concept of pseudo‐direct energy integration (PDEI) which reformulates indirect integration as direct integration using pseudo‐process streams. Two algorithms are presented to achieve energy integration for batch processes operating cyclically (in a campaign mode). The first algorithm targets maximization of energy recovery and overcomes the limitations of some of the existing contributions for design of mixed integrated systems. The second algorithm provides a network reduction methodology to generate a cadre of integrated designs while exploring the trade‐off between capital (number of heat exchangers and storage units) and operating costs (utility consumption). The proposed framework is illustrated using a benchmark example of two hot and two cold streams. © 2017 American Institute of Chemical Engineers AIChE J, 63: 55–67, 2018     

Reducing the effects of failure propagation in periodic processes involving intermediate storage with multiple input/multiple output streams

Batch processes are susceptible to long term production failures that adjacent intermediate storage cannot absorb totally and therefore force the shut-down of adjacent units. Because batch processes have many timing constraints, a careless storage operation leads to the propagation of the failures along the production line which results in a great additional loss of productivity. This article develops operational algorithms for the basicMIMO storage system in the presence of failures of the processing units, up or down-stream of the storage facility. Specially, we consider a class of long term failures which affect all or a subset of the multiple input/output streams. Algorithms are carefully designed to satisfy physical constraints and fully utilize the storage capacity, while minimizing the duration of forced shut-downs. An example study simulating failures demonstrates the effectiveness of our approach.     

A hybrid system of heuristics and simulated annealing for large size scheduling problems of batch processes with pipeless intermediate storage

This paper describes a new scheduling solution for large number multi-product batch processes with complex intermediate storage system. Recently many batch chemical industries have turned their attention to a more efficient system known as a pipeless batch system. But existing plants need to change their systems to pipeless systems, piece by piece. In this case, current systems are changed to pipeless systems by way of non critical process operations such as through the use of intermediate storage. We have taken the conventional batch plant with a pipeless storage system as an objective process. Although the operation of a pipeless storage system becomes more complex, its efficiency is very high. With this system, all of the storage should be commonly used by any batch unit. For this reason, solving the optimal scheduling problem of this system with a mathematical method is very difficult. Despite the attempts of many previous researches, there has been no contribution which solves the scheduling of intermediate storage for complex batch processes. In this paper, we have developed a hybrid system of heuristics and Simulated Annealing (SA) for large multi-product processes using a pipeless storage system. The results of this study show that the performance and computational time of this method are superior to that of SA and Rapid Access Extensive Search (RAES) methods.     

Finished oil handling and storage in the U.S.

Various techniques are practiced in the U.S. to prevent deterioration of vegetable oils following the final stage of processing through deodorization. Because oxidation; free fatty acid development, or adulteration by impurities are the primary concerns, the general practice is to keep oils in closed vessels in an atmosphere that excludes oxygen and moisture and where temperatures are controlled at minimum levels. The technology of sparging and blanketing finished oils with nitrogen during storage and transfer from vessel to vessel is shown. Also, a typical blanketing system for a series of vessels, pressure controllers, and techniques to avoid vacuum conditions is described.     

Scheduling of serial multiproduct batch processes via simulated annealing

We present an in-depth study of the simulated annealing approach to the scheduling of serial multiproduct batch processes under the assumption of a permutation schedule. Four versions of the simulated annealing algorithm are studied based on two move acceptance criteria, the Metropolis algorithm and the Glauber algorithm, and two annealing schedules, the exponential schedule and the Aarts and van Laarhoven schedule. Makespan minimization is performed for unlimited intermediate storage (UIS), no intermediate storage (NIS), zero wait (ZW), finite intermediate storage (FIS) and mixed intermediate storage (MIS) flowshop problems using simulated annealing and also the idle matrix search (IMS) heuristic. Of the four versions of the simulated annealing algorithm studied, the Metropolis algorithm with the Aarts and van Laarhoven annealing schedule is found to give the best results, with all four versions giving significantly better results than the IMS heuristic. The Metropolis algorithm with the Aarts and van Laarhoven annealing schedule is studied in more detail for further comparison with the IMS heuristic in terms of the computational effort expended by the simulated annealing algorithm and the solution quality obtained.     

Intermediate storage in batch/continuous processing systems under stochastic operation conditions

A mathematical model and model-based method is presented to design the intermediate storages aiming to buffer the operational differences between the batch and continuous subsystems in processing systems. The occurrence times of the inputs are assumed to be described by a Poisson process, while the amounts of the material transferred by the batch units allowed changing according to general probability distributions. Based on the stochastic differential equation model of operation, integral equations for determining the overflow and underflow probabilities of a finite storage are formulated for both infinite and finite operation horizons that provide the basis for the rational design of such intermediate storages. Analytical solutions to the integral equations for infinite horizons are derived in the cases of constant and exponentially distributed inputs. For the batch sizes described by general distribution functions, solutions to the integral equations are obtained in the form of approximating functions generated by stochastic simulation. A number of numerical experiments with exponential, normal and lognormal distributions of the batch sizes are presented and analyzed. The effects of process parameters on the design are also investigated.     

除盐水系统建模与物料衡算分析

新鲜水的工业除盐系统通常涉及膜分离（例如超滤、反渗透等），阴阳离子交换树脂床和储罐等。其中离子交换和膜分离单元可看作单入口双出口的半连续过程单元，具有间歇用水过程的特征。然而，尚未有关于除盐水系统的间歇水网络综合的研究报告。对除盐水系统中双出口半连续单元和水箱分别建立流量衡算、杂质质量衡算模型和储罐模型。根据不同工况下除盐水的需求量，利用GAMS软件平台对建立的数学模型进行求解，得出除盐水系统中每个储罐的容量和对应的新鲜水用量。进一步根据储罐最大容量需求，设计出满足不同工况条件下储罐容量。简化的工业案例研究验证了所提出模型的有效性。     

A graphical technique for the design of water-using networks in batch processes

This paper presents a graphical technique for the design of water-using networks in batch plants. Water integration is achieved by exploiting all possibilities of water reuse/recycle to minimize not only freshwater consumption, but also wastewater generation. Since time limitation for unmatched operating periods may be the primary barrier to the integration in batch processes, the installation of storage facilities is quite common to enhance the water recovery. For that reason, the cost in terms of storage facilities becomes another issue to be considered. This work is focused on network design, like the second stage of conventional pinch analyses. Some useful concepts and principles addressed in literatures are adopted to help the design of batch water network and to ensure the maximum recovery, thus the utility usage, the network structure and the storage policy can be obtained through the analysis. Once the freshwater expenditure is determined, workable ways are sought to cut the number of storage tanks and they also reduce the network complexity. In the context of this paper, a hybrid system that includes different type of water-using operations with distinct operating modes is taken into account to display the versatility of proposed approach. Furthermore, considering the fact that sometimes water reuse/recycle between certain operations is not allowed to prevent operational problems, the action of network design should be more deliberate owing to additional restraints. Therefore, the potential for water integration may be diminished, which means a less amount of water recovery. Finally, an illustrative example is provided to amplify the application of proposed approach. Like most graphical techniques, the presented work is restricted to a single key contaminant.     

Detailed design of multipurpose batch plants

A formulation is presented for the optimal selection of both the equipment units and the network of connections for multipurpose batch plants so as to satisfy given production requirements for a variety of products. The model includes very general constraints and objective functions and permits to optimize simultaneously the structural aspects of the plant and the associated production schedule, accounting for both capital costs of equipment units and pipework, operating costs and revenues. A special novelty of the formulation is that it provides the possibility of generating directly the optimal connectivity between the process units, optimal sizing and costs of the transfer lines, and the optimal storage policies (and associated vessel sizes, if any) for stable intermediates without the need for a priori assumptions (e.g. unlimited storage, etc.).The resulting MILP problem is solved using a branch and bound method. Several examples are detailed, demonstrating the generality of the approach and the importance of including structural and operational aspects at the design stage.The flexibility of the formulation permits utilizing various design strategies, from a simultaneous optimization of all problem decisions (equipment, connections and schedule) to a sequential optimization of main equipment, followed by the design of connections etc. These strategies are also illustrated by an example.     

A two-stage approach for the synthesis of inter-plant water networks involving continuous and batch units

This paper presents a mathematical optimization model for inter-plant water network (IPWN) synthesis, where process units operate in mixed continuous and batch modes. The current developed model consists of a two-stage approach, and is dedicated to the special case where there are more continuous than batch units. In the first stage, all batch units are treated as continuous units by using auxiliary water storage tanks, and a continuously operated IPWN is synthesized to minimize the fresh water consumption. Subject to the determined IPWN flow rates, the water storage policy for the batch units is determined in the second stage to minimize the total storage capacity. Alternatively, the formulations of both stages can be combined and solved simultaneously to minimize the IPWN cost. Two modified literature examples are used to illustrate the proposed approach.